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The presence of an unsaturated region beneath a streambed during groundwater pumping near streams can reduce the pumping capacity, change flow paths, and alter the types of biological transformations in the streambed sediments. A three‐dimensional, multiphase flow model of two horizontal collector wells along the Russian River near Forestville, California, was developed to investigate the impact of varying the ratio of the aquifer to streambed permeability on (1) the formation of an unsaturated region beneath the stream, (2) the pumping capacity, (3) stream water fluxes through the streambed, and (4) stream water traveltimes to the collector wells. The aquifer to streambed permeability ratio at which the unsaturated region was initially observed ranged from 10 to 100. The size of the unsaturated region beneath the streambed increased as the aquifer to streambed permeability ratio increased. The simulations also indicated that for a particular aquifer permeability, decreasing the streambed permeability by only a factor of 2–3 from the permeability where desaturation initially occurred resulted in reducing the pumping capacity. In some cases, the stream water fluxes increased as the streambed permeability decreased. However, the stream water residence times increased and the fraction of stream water that reached that the wells decreased as the streambed permeability decreased, indicating that a higher streambed flux does not necessarily correlate to greater recharge of stream water around the wells.